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Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Find the location of all decimal points in the dividend n and divisor m. If necessary, simplify the long division problem by moving the decimals of the divisor and dividend by the same number of decimal places, to the right (or to the left), so that the decimal of the divisor is to the right of the last digit.
A common technique for multiplication with larger numbers is called long multiplication. This method starts by writing the multiplier above the multiplicand. The calculation begins by multiplying the multiplier only with the rightmost digit of the multiplicand and writing the result below, starting in the rightmost column.
On currently available processors, a bit-wise shift instruction is usually (but not always) faster than a multiply instruction and can be used to multiply (shift left) and divide (shift right) by powers of two. Multiplication by a constant and division by a constant can be implemented using a sequence of shifts and adds or subtracts. For ...
The lattice technique can also be used to multiply decimal fractions. For example, to multiply 5.8 by 2.13, the process is the same as to multiply 58 by 213 as described in the preceding section. To find the position of the decimal point in the final answer, one can draw a vertical line from the decimal point in 5.8, and a horizontal line from ...
Dividing integers in a computer program requires special care. Some programming languages treat integer division as in case 5 above, so the answer is an integer. Other languages, such as MATLAB and every computer algebra system return a rational number as the answer, as in case 3 above. These languages also provide functions to get the results ...
To change a common fraction to a decimal, do a long division of the decimal representations of the numerator by the denominator (this is idiomatically also phrased as "divide the denominator into the numerator"), and round the answer to the desired accuracy. For example, to change 1 / 4 to a decimal, divide 1.00 by 4 (" 4 into 1.00 ...
Multiplication is a mathematical operation of repeated addition. When two numbers are multiplied, the resulting value is a product. The numbers being multiplied are multiplicands, multipliers, or factors. Multiplication can be expressed as "five times three equals fifteen," "five times three is fifteen," or "fifteen is the product of five and ...